It seems like Jaunty is not being maintained anymore. When trying to install the chrome package:

steven@steven-desktop ~/Desktop $ sudo dpkg -i google-chrome-stable_current_i386.deb
Selecting previously deselected package google-chrome-stable.
(Reading database ... 106471 files and directories currently installed.)
Unpacking google-chrome-stable (from google-chrome-stable_current_i386.deb) ...
dpkg: dependency problems prevent configuration of google-chrome-stable:
google-chrome-stable depends on libasound2 (>> 1.0.22); however:
Version of libasound2 on system is 1.0.18-1ubuntu9.
google-chrome-stable depends on libc6 (>= 2.11); however:
Version of libc6 on system is 2.9-4ubuntu6.
google-chrome-stable depends on libcups2 (>= 1.4.0); however:
Version of libcups2 on system is 1.3.9-17ubuntu1.
google-chrome-stable depends on libdbus-1-3 (>= 1.2.14); however:
Version of libdbus-1-3 on system is 1.2.12-0ubuntu2.
google-chrome-stable depends on libfontconfig1 (>= 2.8.0); however:
Version of libfontconfig1 on system is 2.6.0-1ubuntu12.
google-chrome-stable depends on libgconf2-4 (>= 2.27.0); however:
Version of libgconf2-4 on system is 2.26.0-0ubuntu1.
google-chrome-stable depends on libgcrypt11 (>= 1.4.2); however:
Version of libgcrypt11 on system is 1.4.1-2ubuntu1.
google-chrome-stable depends on libgtk2.0-0 (>= 2.18.0); however:
Version of libgtk2.0-0 on system is 2.16.1-0ubuntu2.
google-chrome-stable depends on libnss3-1d (>= 3.12.3); however:
Version of libnss3-1d on system is 3.12.2~rc1-0ubuntu2.
google-chrome-stable depends on libstdc++6 (>= 4.4.0); however:
Version of libstdc++6 on system is 4.3.3-5ubuntu4.
google-chrome-stable depends on libatk1.0-0 (>= 1.30.0); however:
Version of libatk1.0-0 on system is 1.26.0-0ubuntu2.
dpkg: error processing google-chrome-stable (--install):
dependency problems - leaving unconfigured
Processing triggers for man-db ...
Errors were encountered while processing:
google-chrome-stable

It seems like there is no way for me to update all of these libraries to the correct versions anymore because they all report being already updated.

steven@steven-desktop ~/Desktop $ sudo apt-get install libasound2
Reading package lists... Done
Building dependency tree
Reading state information... Done
libasound2 is already the newest version.
You might want to run `apt-get -f install' to correct these:
The following packages have unmet dependencies:
google-chrome-stable: Depends: libasound2 (> 1.0.22) but 1.0.18-1ubuntu9 is to be installed
Depends: libc6 (>= 2.11) but 2.9-4ubuntu6 is to be installed
...

What can I do? Try to dig up a .deb of the most recent version of Chrome which does not require dependencies more recent than what is available on Jaunty? Am i likely to ever succeed with this?

The reason I chose a distro based on Jaunty is because Jaunty is nice and stable. I figured that would help me succeed in getting npm, node.js package manager, working. I'll want an updated Chrome to test that... This is an awful bit of catch-22...

Google's Chrome packages no longer support these releases; the required version of Ubuntu is not 10.04, the current long-time support release. (The previous LTS release, 8.04 hardy, is still supported on servers but not on desktops.)

If you want to install recent programs, you'll need to have a more recent distribution. If you're after stability, I recommend Ubuntu LTS (upgrades every 2 years, with a ~1yr grace time) or Debian stable (upgrades every 2–3 years, with a few months' grace time).